The Texas Supreme Court has ruled that the execution of Robert Roberson, convicted in his daughter’s “shaken baby” death, can’t be stopped by a legislative subpoena, after lawmakers made a last-ditch effort to pause the process.

Roberson was scheduled to die by lethal injection on Oct. 17. Texas lawmakers, hoping to buy him more time, issued a subpoena the day before to have him testify at the Texas Capitol on a date after his planned execution.

After a flurry of legal wrangling in state criminal and civil courts that started less than two hours before he was to die and ended just before midnight, the Texas Supreme Court issued a temporary ruling in Roberson’s favor. The decision paused his execution so he could comply with the subpoena and testify to a bipartisan House committee.

On Friday, the Texas Supreme Court said that while the state’s legislative branch was within its rights to compel testimony from Roberson, it doesn’t have the power to override the legal process leading to an execution.

Given that lawmakers had ample time before Roberson’s execution to question him, their “interest in obtaining testimony must yield if the other branches are unwilling to dismantle a scheduled execution,” the court ruled.

Roberson’s case has drawn wide support, including from Texas lawmakers and the bestselling author John Grisham . They have argued that his conviction was based on a faulty medical theory—shaken baby syndrome—that has since been reassessed. In recent years, the medical testimony in a number of shaken-baby syndrome cases has come under scrutiny .

The Texas Department of Criminal Justice declined to comment. Roberson’s lawyer said she hoped the pause caused by the subpoena allowed those in power to re-evaluate the medical evidence against her client.

“Given the overwhelming new evidence of innocence, we ask the State of Texas to refrain from setting a new execution date,” said attorney Gretchen Sween.

To set a new date, Anderson County’s district attorney must file a motion with the trial court. The judge would pick the date, which must be at least 90 days out.

The district attorney didn’t respond to a request for comment.

Democratic state Rep. Joe Moody, chairman of the Texas House committee on criminal jurisprudence, and Jeff Leach, a Republican legislator, said the Texas Supreme Court ruling made it clear the committee acted within its powers when it subpoenaed Roberson. Although Roberson didn’t end up testifying after his execution was delayed, the lawmakers said they hope it can happen now.

“The Supreme Court strongly reinforced our belief that our committee can indeed obtain Mr. Roberson’s testimony and made clear that it expects the executive branch of government to accommodate us in doing so. That has been our position all along,” the statement said.

Roberson, convicted in 2003 for the killing of his 2-year-old daughter, Nikki Curtis, in Palestine, Texas, is the first person facing execution in a shaken-baby syndrome case, according to his lawyers and the Center for Integrity in Forensic Sciences, which tracks such cases.

Roberson has maintained his innocence and his lawyers have said his daughter, who was ill at the time, died from complications from double pneumonia. She had fallen from her bed not long before Roberson brought her to the local emergency room, according to his lawyers.

Roberson has lost several appeals, and the U.S. Supreme Court on Oct. 17 declined to halt Roberson’s execution. Texas Gov. Greg Abbott, a Republican, didn’t respond to requests for a 30-day reprieve from Roberson’s lawyers, and he opposed the lawmakers’ subpoena in a brief filed with the Texas court on Oct. 20.

“Unless the Court rejects that tactic, it can be repeated in every capital case, effectively rewriting the Constitution to reassign a power given only to the Governor,” said the brief, submitted by the governor’s general counsel.